The dot product calculator allows the calculation of the dot product of two vectors online.

dot_product online

- Analytical definition of the scalar product
- Property
- Online calculation of the scalar product.
- Dot product calculation from numeric coordinates.
- Dot product calculation from literal coordinates.

It is possible to calculate the **dot product of two vectors** from their coordinates.
In the plan, in an orthonormal system `(O,vec(i),vec(j))` ,
`vec(u)` is a vector of coordinates (x,y) and `vec(v)` is a vector of coordinates (x',y'),
the **dot product** is given by the formula
xx'+yy'=0.

This definition can be extended to space. In a direct orthonormal system `(O,vec(i),vec(j),vec(k))`,
`vec(u)` is a vector of coordinates (x,y,z) and `vec(v)` is a vector of coordinates (x',y',z'),
the **dot product** is given by the formula
xx'+yy'+zz'=0.

If `vec(u)` and `vec(v)` are orthogonal, then the dot product is zero.

The **dot product calculator** allows to calculate the dot product of two vectors from their coordinates.
The **calculation of the scalar product online** can be done with numbers or literal expressions.

To calculate the dot product of the following vectors `vec(v)` [1;5] and `vec(u)` [1;3], enter dot_product(`[1;5];[1;3]`). After calculation the result 16 is returned.

To calculate the dot product of the following vectors `vec(v)` `[a;b-1]` and `vec(u)` `[2a;a/2]`, enter dot_product(`[a;b-1];[2a;a/2]`). After calculation the result `-a/2+(b*a)/2+2*a^2` is returned.

The dot product calculator allows the calculation of the dot product of two vectors online.

See also :

- Cross product : cross_product. The vector calculator allows the calculation of the cross product of two vectors online.
- Calculate dot product : dot_product. The dot product calculator allows the calculation of the dot product of two vectors online.
- Product of a vector by a number : product_vector_number. The vector calculator allows to calculate the product of a vector by a number online.
- Calculus scalar triple product : scalar_triple_product. The scalar_triple_product function allows online calculation of scalar triple product.
- Vector calculator : vector_calculator. The vector calculator allows to do calculations with vectors using coordinates.
- Calculating the coordinates of a vector from two points. : vector_coordinates. The vector calculator allows the calculation of the coordinates of a vector from the coordinates of two points online.
- Calculating the difference of two vectors : vector_difference. The vector_difference function is used to calculate the difference of two vectors online.
- Calculating the norm of a vector : vector_norm. The vector calculator allows the calculation of the norm of a vector online.
- Calculating the sum of two vectors : vector_sum. The vector calculator allows the calculation of the sum of two vectors online.